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Schifter, Deborah (Ed.):
What’s Happening in Math Class?
Vol. 2: Reconstructing Professional
Identities
New York: Teachers College Press, 1996. – 204 p.
ISBN 0-8077-3483-7 (paper)
ISBN 0-8077-3484-5 (cloth)
Michael Price, Leicester
This book is the second of two volumes (Schifter 1996)
resulting from the work of the Mathematics Process Writing Project (MPWP) in the United States of America. The
project was directed over a three-year period (1990–1993)
by Deborah Schifter of the Center for the Development of
Teaching at the Education Development Center in Newton
(Massachusetts) and was an extension of the work of the
SummerMath for Teachers courses at Mount Holyoke College in South Hadley (Massachusetts) which Schifter directed from 1988 to 1993. The MPWP involved 48 teachers (44 women and four men) in the production of narratives (49 are mentioned on p. 5) about their classroom
experiences in mathematics. In the first volume, 13 narratives were published and the second volume here under
review includes nine narratives from elementary school
teachers spanning Grades Kindergarten through 6. Four
mathematics teacher educators provide commentaries on
three pairs and one trio of narratives. Schifter provides
an introduction, a conclusion and two appendices which
helpfully include details of the structure of the MPWP
courses, and the reading and writing assignments given to
the participants.
In order to understand the significance of this book for
the international development of mathematics education
it is necessary to situate it in the context of recent developments in the USA. Schifter (p. 1) refers to “a convergence between changing social needs and two decades
of research in cognitive psychology” which has helped to
shape a new vision of the teaching and learning process in
classrooms. This vision has been embodied in a number of
influential policy documents over the last ten years, including major publications from the Mathematical Association
of America (1991), the National Council of Teachers of
Mathematics (1991) and the National Research Council
(1989, 1990).
Central to this vision is a constructivist view of learning in which each student builds a personal set of meanings for the mathematics in the curriculum as implemented by teachers in the classroom. In the words of
the National Research Council (1989, p. 58–59), for students to understand what they learn “they must enact for
themselves verbs that permeate the mathematics curriculum: ‘examine’, ‘represent’, ‘transform’, ‘solve’, ‘apply’,
‘prove’, ‘communicate’.” This view of the learning process has fundamental implications for both the forms of
student engagement to be promoted in the mathematics
classroom and the role of the teacher as a facilitator in
Book Reviews
such engagement. The emphasis shifts to communication
and collaboration among students in posing questions, formulating conjectures, discussing problems and evaluating
solutions. In all this, the teacher “guided by close analysis of her students’ thinking, frames appropriate problemsolving contexts for them, facilitates discussion of their
mathematical ideas, and steers them toward confrontation
with important conceptual issues” (p. 1).
Translation of the rhetoric associated with this vision
into curriculum reality requires practising teachers to
“construct for themselves practices appropriate to its principles” (p. 1). As Schifter emphasises, such a process is
complex and challenging for teachers, and involves “reconstructing professional identities” which is the subtitle
of the book. As she makes clear, the major motivation
for this book (and its companion volume) was the need
for a “wealth of images” to provide interpretations for the
“rhetorical motifs” of the reform movement (p. 6). The
book provides a public contribution to what should, in
Schifter’s view, be a continuous and unending process of
professional learning about how students learn.
For the teacher contributors themselves, writing about
their own classroom inquiries was an important part
of their personal learning progression, supported by the
MPWP courses. The teachers used tape recording, note
taking, transcription, recollection and discussion with
other teachers to inform their narratives. On the MPWP
courses the teachers were also provided with formative
reading and writing assignments, and regular feedback
from Schifter, their instructor. Production of the final public narratives was nonetheless “time-consuming, exposing,
and difficult” (p. 175). But the editor expresses the conviction that such writing “represents a form of professional
research uniquely suited to the project of reform” (p. 175)
which the writing was intended to support.
Seven of the nine narratives are presented under three
headings which capture different aspects of the process
of professional reconstruction: teachers as mathematical
thinkers, as managers of the classroom, and as monitors of
student learning. The two other narratives illustrate particular aspects of the new pedagogy and reflective practice
focused on a scheme for graphical work and the use of
student journals, both in Grade 3.
The first two narratives, from Lisa Yaffee and Nora L.
Toney, concentrate on these teachers’ personal mathematics education and the tensions created between their past
experiences and struggles as learners at the receiving end
of mathematics instruction and the challenges of the new
pedagogy as embodied in the summer and MPWP courses.
The two narratives highlight the need to address elementary school teachers’ attitudes and feelings, which they
bring to their own teaching and to in-service courses, as
well as their perceptions of mathematical thinking. Toney,
in particular, opens up and confronts much wider issues
of race and gender which strongly impacted on her own
mathematics education. In her essay on the two narratives,
Deborah Loewenberg Ball draws out some of the implications of these teachers’ autobiographies for strategies to
support the change process, including the potential and
limitations of curriculum materials, courses and teachers’
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writing. These two narratives shed little light on these
teachers’ own classroom practices but, as Ball concludes,
“it is crucial in designing supports for their learning that
teachers’ stories be heard; their experiences, respected; and
their views, solicited” (p. 44).
The two narratives from Karen Schweitzer and Anne
Marie O’Reilly illustrate features of the new patterns of
authority involved in the new pedagogy. As Schifter points
out, “figuring out how to translate the vision into dayto-day instruction ... will be neither smooth nor rapid,
but arduous, sometimes scary, and sometimes exhilarating” (p. 46). Schweitzer’s narrative brings her own classroom to life through lively description, samples of dialogue, and analysis of her Grade 2 students’ responses to
a range of challenging tasks involving practical counting,
grouping and measurement. The excitement, disappointment, confusion and frustration involved in giving these
young students a large measure of choice and control are
well exemplified, and Schweitzer’s growing confidence,
supported by the MPWP course, is evident. By contrast,
O’Reilly’s narrative is strong on self-reflection in relation to the rhetoric for reform but she only provides one
episode from her Grade 6 classroom. Ruth M. Heaton’s
essay on the two narratives emphasises the importance of
these teachers’ feelings about the new patterns of authority in their classrooms, and the value of honest and reflective accounts to support other teachers in the process of
change. In particular she focuses on promoting classroom
discourse and the risks involved, including how to cope
with silence.
The three narratives from Janice M. Szymaszek, Christine D. Anderson and Jessica Dobie Redman illustrate the
process of inquiry into students’ mathematical conceptions
through classroom practice, guided by watching and listening to the students in order to unpack their own lines of
thinking. The linking essay is provided by Stephen Lerman who is quick to point out that “interpreting what
students know from what they say is far from straightforward” (p. 126). Szymaszek and Redman provide rich
accounts of a wide range of counting activities for Kindergarten and Grade 2 students respectively. The element of
surprise in students’ responses and thinking is strong in
both narratives, and the tasks were well chosen to push the
students’ thinking to their limits, with the teachers “leading from behind” (p. 96). Szymaszek’s judgement that her
experience was “glorious and bewildering” (p. 96) is well
substantiated in her account. Redman makes a significant
confession: “Realizing that there were such different levels
of understanding of counting frightened me” (p. 119).
Anderson focuses on shape identification in the Kindergarten. The element of surprise is again strong, notably in
relation to the concepts of side and triangle as exemplified
in different practical contexts. The challenge to draw and
talk about drawing a shape, line by line, also proved to
be particularly productive. Lerman’s essay focuses on the
extent to which these three narratives move from classroom observation, through inquiry into students’ mathematical conceptions, to promote the notion of “teacher as
researcher” (p. 131). The strength of these particular narratives certainly supports this challenging notion.
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The final two narratives are provided by Grade 3 teachers, Valerie Penniman and Deborah Carey O’Brien. Penniman presents a detailed description and analysis of her
ambitious scheme for graphical work. She also steps back
to evaluate its success in terms of a number of aspects
of her own decision making about the students’ role in
the learning process: the degree of challenge, the level of
security, and the extent of students’ self analysis, decision making and ownership of the mathematics. O’Brien
discusses the use of journals both as a tool for students’
learning and as a form of teacher assessment, including
feedback to parents. Her narrative clearly demonstrates
the steepness of the learning curve involved for both the
teacher and her students in making effective use of such
a tool.
Susan Jo Russell’s essay highlights the challenge of reflective practice for the busy and vulnerable classroom
practitioner:
“Taking responsibility for the teaching of mathematics means
examining the complexity of the students’ knowledge, beliefs,
and experience to try to make good guesses about their views of
mathematical ideas, rather than blaming them for being unable
or unwilling to learn.” (p. 158)
She concludes that reflective teaching, as exemplified by
the last two narratives, is “a matter of taking ‘two steps
forward, one step back’, in a continual cycle of experimentation, observation, reflection, and revision” (p. 161).
In the conclusion, Schifter steps back from the set of
narratives to situate them in the context of national priorities for curriculum development in the USA:
“Stories like those collected here must become public; their
telling, commonplace. For the kind of transformation teachers
are being asked to undertake is so profound, the challenges to
their professional ways of being so threatening, that without some
larger perspective that contextualizes their difficulties, and without the reassuring knowledge that others have worked through
similar confusions, most will despair of success when the going
gets rough, and many once again will retreat behind the closed
doors of the classroom.” (p. 164)
As an English reviewer I am struck by the extent to which
such priorities for mathematics curriculum development
in the USA are no longer matched by those prevailing in
England in the late 1990s. Classroom teachers’ reflections
and writing about English students’ learning have largely
been eroded since the 1980s by external political pressures
both for accountability, through the National Curriculum,
tests and inspection, and for more emphasis on effective
methods of instruction to achieve better results in national
and international performance tables, based on pencil-andpaper tests.
I welcome this book, which puts the learners at the centre of the classroom enterprise. The contributions have
been well prepared, organised and edited, and I would
value further collections along similar lines. But I regret
that such a book is unlikely to be produced in English conditions up to the next millennium. The notion of “teachers
leading from behind” would not appeal to English politicians (including the new Labour government), and the subtleties and complexities of such a notion would largely be
lost on the public at large, who represent the consumers
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in education. The significance of the book under review
is largely determined by the national context within which
it was created.
References
Mathematical Association of America (1991): A call for change:
Recommendations for the mathematical preparation of teachers. – Washington, DC: MAA
National Council of Teachers of Mathematics (1991): Professional standards for teaching mathematics. – Reston, VA:
NCTM
National Research Council (1989): Everybody counts: A report
to the nation on the future of mathematics education. – Washington, DC: National Academy Press
National Research Council (1990): Reshaping school mathematics: A framework for curriculum. – Washington, DC: National
Academy Press
Schifter, D. (Ed.) (1996): What’s happening in math class?
Vol. 1: Envisioning new practices through teacher narratives.
– New York: Teachers College Press
Author
Price, Michael H., Dr., University of Leicester, School of Education, 21 University Road, Leicester LE1 7RF, England.
mhp3@leicester.ac.uk
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